29 research outputs found
Lyapunov exponents, entropy production and decoherence
We establish that the entropy production rate of a classically chaotic
Hamiltonian system coupled to the environment settles, after a transient, to a
meta-stable value given by the sum of positive generalized Lyapunov exponents.
A meta-stable steady state is generated in this process. This behavior also
occurs in quantum systems close to the classical limit where it leads to the
restoration of quantum-classical correspondence in chaotic systems coupled to
the environment.Comment: 4 ReVTeX pages + 3 postscript figures. PRL (to appear
Chaos and Lyapunov exponents in classical and quantal distribution dynamics
We analytically establish the role of a spectrum of Lyapunov exponents in the
evolution of phase-space distributions . Of particular interest is
, an exponent which quantifies the rate at which chaotically
evolving distributions acquire structure at increasingly smaller scales and
which is generally larger than the maximal Lyapunov exponent for
trajectories. The approach is trajectory-independent and is therefore
applicable to both classical and quantum mechanics. In the latter case we show
that the limit yields the classical, fully chaotic, result for the
quantum cat map.Comment: 5 RevTeX pages + 2 ps figs. Phys. Rev. E (to appear,'97
Exponentially rapid decoherence of quantum chaotic systems
We use a recent result to show that the rate of loss of coherence of a
quantum system increases with increasing system phase space structure and that
a chaotic quantal system in the semiclassical limit decoheres exponentially
with rate , where is a generalized Lyapunov exponent.
As a result, for example, the dephasing time for classically chaotic systems
goes to infinity logarithmically with the temperature, in accord with recent
experimental results.Comment: 4 ReVTeX pages + 1 postscript figure. PRL (to appear
Non-monotonicity in the quantum-classical transition: Chaos induced by quantum effects
The transition from classical to quantum behavior for chaotic systems is
understood to be accompanied by the suppression of chaotic effects as the
relative size of is increased. We show evidence to the contrary in the
behavior of the quantum trajectory dynamics of a dissipative quantum chaotic
system, the double-well Duffing oscillator. The classical limit in the case
considered has regular behavior, but as the effective is increased we
see chaotic behavior. This chaos then disappears deeper into the quantum
regime, which means that the quantum-classical transition in this case is
non-monotonic in .Comment: 4 pages; presentation modified significantly to demonstrate that
quantum effects are indeed responsible for the `anomalous' chaos. 2 figures
adde
Parameter scaling in the decoherent quantum-classical transition for chaotic systems
The quantum to classical transition has been shown to depend on a number of
parameters. Key among these are a scale length for the action, , a
measure of the coupling between a system and its environment, , and, for
chaotic systems, the classical Lyapunov exponent, . We propose
computing a measure, reflecting the proximity of quantum and classical
evolutions, as a multivariate function of and searching for
transformations that collapse this hyper-surface into a function of a composite
parameter . We report results
for the quantum Cat Map, showing extremely accurate scaling behavior over a
wide range of parameters and suggest that, in general, the technique may be
effective in constructing universality classes in this transition.Comment: Submitte